Machine Learning - Assignment 1

Author: Benjamin Brodwolf (benjamin.brodwolf@students.fhnw.ch)

Task 1

Task 2

% loading the prices and sqft_living

prices = table2array( data(:,"price") );

sqft_living = table2array( data(:, "sqft_living"));

figure;

% Plot the data sqft_living and prices

plot(sqft_living, prices, 'o', 'MarkerSize', 1);

title({'Task2','Plot Price & Square feet of Living'});

ylabel('House Prices on 10,000s');

xlabel('Living Areas Sq. Ft.');

m = length(prices);

% Add intercept term to sqliving

sqft_living = [ones(m, 1) sqft_living];

% Estimate the prices with sqft_living

theta = normalEqn(sqft_living, prices);

fprintf('Theta computed from the normal equations:\n%f,\n%f',theta(1),theta(2))

Theta computed from the normal equations: -43580.743095, 280.623568

% Plot the linear fit

hold on; % keep previous plot visible

plot(sqft_living(:,2), sqft_living*theta, 'r-');

legend('Livin area data', 'Linear regression');

hold off;

prices_pred = sqft_living*theta;

residual = prices - prices_pred;

tukeyAnscombePlot(prices_pred, residual, "2");

Above and under the "Zero Line" Top: 9724 Bottom: 11889 Std.dev.: 1530.886181

• The points should be evenly distributed around the 'Zero Line'
• The Cone-shape

Task 3

Plot log(prices) with Square Feets of living with Lineare Regression

figure;

hold on; % for new figure

plot(sqft_living(:,2), prices_log, 'o', 'MarkerSize', 1); % Plot the data

title({'Task 3',' Plot log(Prices) & Square feets of living'});

ylabel('Log(Prices)');

xlabel('Living Areas Sq. Ft. 10,000s');

plot(sqft_living(:,2), sqft_living*theta_log, 'r-')

legend('Livin area data', 'Linear regression')

Plot Tukey Anscomble Plot

residual_log = prices_log - prices_log_pred;

tukeyAnscombePlot(prices_log_pred, residual_log, "3");

Above and under the "Zero Line" Top: 11114 Bottom: 10499 Std.dev.: 434.870670

Create a histogram of the residuals (number of bins = 100).

figure;

nbins = 100;

histogram(residual_log, nbins);

title({'Task 3',' Histogram: log(Residuan) & Number of Bins (100)'})

ylabel('log(Residuen)'); % Set the y-axis label

xlabel('number of bins'); % Set the x-axis label

hold on;

Task 4

% "Absolute Percentage Error (APE)" of Task 3.

prices_log = log(prices);

LOG_APE = abs( (prices_log-prices_log_pred)./prices_log );

LOG_MAPE = mean( LOG_APE );

fprintf('The MAPE of Task 3 is %f (%4.2f%%) ' , LOG_MAPE, LOG_MAPE*100); % MAPE is 0.023597 -> 2.36%

The MAPE of Task 3 is 0.023597 (2.36%)

LOG_MdAPE = median( LOG_APE );

fprintf('The MdAPE of Task 3 is %f (%4.2f%%) ' , LOG_MdAPE, LOG_MdAPE*100); % MdAPE is 0.020879 -> 2.09%

The MdAPE of Task 3 is 0.020879 (2.09%)

% "Absolute Percentage Error (APE)" of Task 2.

APE = abs( (prices-prices_pred)./prices );

figure;

hold on;

grid on;

ksdensity(APE);

ksdensity(LOG_APE);

title({'Task 4',' Kernel Distribution of the APE of Task 2 & 3'});

legend('APE with price (Task2)', 'APE with log(price) (Task3)');

ylabel('Density'); % Set the y-axis label

xlabel(' APE '); % Set the x-axis label

hold off;

Task 5

Scatter plot with 'zipcode':

amount_of_zipcode = num2str(length(unique(zipcode)))

amount_of_zipcode = '70'

% scale zipcode between 1 to 0 for coloring

min_zipcode = min(zipcode);

max_zipcode = max(zipcode);

color = (zipcode - min_zipcode) ./ (max_zipcode-min_zipcode);

figure;

geoscatter(lat, long, zipcode./50000 ,color, 'filled');

cbar = colorbar('Ticks', [0, 1], ...

'TickLabels', { num2str(min(zipcode), '%d') , num2str(max(zipcode), '%d')}, ...

'TickLabelInterpreter', "tex");

ylabel(cbar, ' Zipcode');

title(['Task 5: GeoScatter-Plot of ', amount_of_zipcode ,' Zipcodes']);

Scatter plot with 'price':

% scale prices between 1 to 0 for coloring

min_price = min(prices);

max_price = max(prices);

color = (prices - min_price) ./ (max_price-min_price);

figure;

geoscatter(lat, long, prices./200000 ,color, 'filled');

cbar = colorbar('Ticks', [0, 0.25 0.5, 0.75 1], ...

'TickLabels', { num2str(min(prices), '%d'), num2str(max(prices)*0.25, '%d') , num2str(max(prices)*0.5, '%d') , num2str(max(prices)*0.75, '%d') , num2str(max(prices), '%d')}, ...

'TickLabelInterpreter', "tex");

ylabel(cbar, 'Prices');

title({'Task 5',' GeoScatter-Plot of House-Prices'});

Scatter plot with 'price' zoomed:

figure;

geoscatter(lat, long, prices./200000 ,color, 'filled');

cbar = colorbar('Ticks', [0, 0.25 0.5, 0.75 1], ...

'TickLabels', { num2str(min(prices), '%d'), num2str(max(prices)*0.25, '%d') , num2str(max(prices)*0.5, '%d') , num2str(max(prices)*0.75, '%d') , num2str(max(prices), '%d')}, ...

'TickLabelInterpreter', "tex");

ylabel(cbar, 'Prices');

title({'Task 5','GeoScatter-Plot of House-Prices','(Zoomed closer to the expensive areas - Center of Seattle)'});

geolimits([47.551 47.726],[-122.340 -122.054])

Task 6